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2A spectrum, or part of a spectrum, which has less power at higher frequencies, is often called "red," and one that has less power at lower frequencies, "blue." A spectrum that has the same power at all frequencies is called "white." These terms are widely used but imprecisely defined.

FIGURE 12.3. (a) The theoretical spectrum, Eq. 12-2, graphed on a log-log plot. The vertical grey dotted line indicates the frequency mc/2n where mc = X/yo and is measured in cycles per year (cpy). For the parameters chosen in the text, mc = 300^, and so the grey line is drawn at a frequency of f60"c[ = 0.19 cpy. (b) Log-log plot of the power spectrum of atmospheric temperature at 500 mbar (black) and SST (grey) associated with the North Atlantic Oscillation, the leading mode of climate variability in the Atlantic sector. See Czaja et al (2003) for more details. The frequency is again expressed in cpy as in (a), and the power in K2 /cpy.

FIGURE 12.3. (a) The theoretical spectrum, Eq. 12-2, graphed on a log-log plot. The vertical grey dotted line indicates the frequency mc/2n where mc = X/yo and is measured in cycles per year (cpy). For the parameters chosen in the text, mc = 300^, and so the grey line is drawn at a frequency of f60"c[ = 0.19 cpy. (b) Log-log plot of the power spectrum of atmospheric temperature at 500 mbar (black) and SST (grey) associated with the North Atlantic Oscillation, the leading mode of climate variability in the Atlantic sector. See Czaja et al (2003) for more details. The frequency is again expressed in cpy as in (a), and the power in K2 /cpy.

and Pacific Oceans, where it is evident, among other things, in occasional failures of the Indian monsoon, extensive droughts in Indonesia and much of Australia, and in unusual rainfall and wind patterns right across the equatorial Pacific Ocean as far as South America and extending beyond the tropics. This phenomenon has been known for a long time. For example, Charles Darwin, in Voyage of the Beagle (1831-1836), noted the tendency for climatic anomalies to occur simultaneously throughout the tropics. Tropical climate variability was first comprehensively described in the 1920s by the meteorologist Gilbert Walker, who gave it the name Southern Oscillation.

Manifestations of interannual variability are not, however, confined to the atmosphere. The El Nino phenomenon has been known for centuries to the inhabitants of the equatorial coast of Peru. Until the middle of the 20th century, knowledge of this behavior was mostly confined to the coastal region, where an El Nino is manifested as unusual warmth of the (usually cold) surface waters in the far eastern equatorial Pacific (see Fig. 9.14), and is accompanied (for reasons to be discussed below) by poor fishing and unusual rains.3 With the benefit of modern data coverage, it is clear that the oceanic El Nino and the atmospheric Southern Oscillation are manifestations of the same phenomenon, which is now widely known by the concatenated acronym ENSO. However, this was not always the case. It was not until the 1960s that Jacob Bjerknes4 argued that the two phenomena are linked.

12.2.2. "Normal" conditions— equatorial upwelling and the Walker circulation

As discussed in Chapter 7, the lower tropical atmosphere is characterized by easterly trade winds, thus subjecting the tropical ocean to a westward wind stress (see, for example, Figs. 7.28b and 10.2). Let us begin by considering a hypothetical ocean on an Earth with no continents, and with a purely zonal, steady, wind stress t < 0 that is independent of longitude, acting on a two-layer ocean with a quiescent deep layer of density p1, capped by a mixed layer of depth h and density p2 = pi - Ap, as sketched in Fig. 12.4.

The dynamics of Ekman-driven upwell-ing and downwelling was discussed in Section 10.1. Here, near the equator, we must modify it slightly. As the equator is approached, the Coriolis parameter diminishes to zero and cannot be assumed to be constant. Instead we writef = 2Q sin < ~ py, where y = a< is the distance north of the equator, and p = 2Q/a = 2.28 x 10-11m-1 s-1 is the equatorial value of the gradient of the Coriolis parameter. The steady zonal

FIGURE 12.4. Schematic of a two-layer ocean model: the upper layer of depth h has a density p2, which is less than the density of the lower layer, p1. A wind stress t blows over the upper layer.

3The name ''El Nino''—the child (and, by implication, the Christ child)—stems from the observation of the annual onset of a warm current off the Peruvian coast around Christmas. El Nino originally referred to this seasonal warm current that appeared every year, but the term is now reserved for the large-scale warming which happens every few years. The opposite phase—unusually cold SSTs in the eastern equatorial Pacific—is often now referred to as La Nina.

Jacob Bjerknes (1897—1975), Norwegian-American meteorologist and Professor at UCLA; son of Vilhelm Bjerknes, the Norwegian pioneer of modern meteorology. Jacob was the first to realize that the interaction between the ocean and atmosphere could have a major impact on the circulation of the atmosphere. He described the phenomenon that we now know as El Nin o.

equation of motion is, from Eq. 10-3, anticipating a weak circulation and so neglecting nonlinear advective terms and replacing f by Py.

Now, since the wind stress is assumed independent of x, we look for solutions such that all variables are also independent of x, in which case the pressure gradient term in Eq. 12-3 vanishes, leaving

Pref dz

If the deep ocean is quiescent, t must vanish below the mixed layer; so the above equation can be integrated across the mixed layer to give

Twindx prf

which simply states that the Coriolis force acting on the depth-integrated mixed layer flow is balanced by the zonal component of the wind stress rwind.

In response to the westward wind stress (t < 0) associated with the easterly tropical trade winds, the flow above the thermo-cline will be driven northward north of the equator (y > 0), and southward for y < 0; there is therefore divergence of the flow and consequent upwelling near the equator, as shown in Fig. 12.5. In fact, most of this upwelling is confined to within a few degrees of the equator. In the extratrop-ics, we saw that the adjustment between the mass field and the velocity field in a rotating fluid sets a natural length scale, the deformation radius, L = \[ghIf, where

wind stress wind-driven divergent flow <- -►

Ocean induced upwelling

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